rr .A.04 620 COLD REGIONS RESEARCH AND ENGINEERING LAB HANOVER NH F/4 8/12IMODELING OF ANISOTRO I CNELECTROMAGNETIC REFLECTION FROM SEA ICE--ETC U)IOCT 80 K N GOLDEN, S F ACKLEY NSF-OPP77-24526

UNCL7ASSIFIED CRREL-GG8-23 NL

Modeling of anisotropic electromagneticreflection from sea ice

01 AD A09 4 6 2 0

tibLJAENTi A

IX o

X4

I or conversion of SI metric units to U.S. Britishcustomary units of measurement consul AS IMStandard [ 180. Metric Pra( tice (Alide, publishedhv the American Society ior Testing and Materi-

,ls. 1916 Race St., Philadelphia, Pa. 1910?.

'

!(n'er Photomicrograph of a thin section of sea

ice illustrating brine pocket shapes. (Photo-graph from CRRfL Research Report 269 byV1 4vek s and A. Assur.)

t(

CRREL Report 80-23

Modeling of anisotropic electromagneticreflection from sea ice

Kenneth M. Golden and Stephen F. Ackley

October 1980

,!

P're'pared for

NATIONAl S(I[N(I FOUNDATION

UNIIID SA][S ARMYt CORPS OF I N('IN[ [RS

(() O) RIGIONS RI SI ARCH AND F NGINt i RING LABORATORYIIANOVI R, NI W HAMPSHIRI. U S A

A pt rblh rI, t, h.l

- i lJncifipd

SECURITY CLASSIFICATION OF THIS PAGE (When Date Entered)

REPORT DOCUMENTATION PAGE READ INSTRUCTIONSBEFORE COMPLETING FORM.' RBEPTN~4Je--- "

. 2. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER

/ ~ CRRELU 0-23 1 .!5?

4.Il fnd Subtitle) .. TYPE OF REPORT 8 PERIOD COVERED

_-MODELING OF ANISOTROPIC ELECTROMAGNETICREFLECTION FROM" SEA ICEz ... EFRIGOG OTNME

6. PERFORMING ORG. REPORT NUMBER

7. AUT HQ.foJ .. 8. CONTRACT OR GRANT NUMBER(s)

Kt . National Science Foundation, DivisionL ent .oena S ephe IFA.kLey.eo a pof Polar Programs Grant DPP77-24528

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASK

U.S. ArmyCold Regions Research and Engineering Laboratory AR&k _WORK UNIT NUMBERS

Hanover, New Hampshire 03755 I

I I. CONTROLLING OFFICE NAME AND ADDRESS 12 RF

National Science Foundation 0ctNW80 /

Washington, D.C. . 3. NUMBER OF PAGES21

14. MONITORING AGENCY NAME & AODRESS(if different from Controlling Office) 15. SECURITY CLASS. (of this report)

Unclassified

IS. DECLASSIFICATION/DOWNGRADINGSCHEDULE

16. DISTRIBUTION STATEMENT (of this Report)

Approved for public release; distribution unlimited.

17. DISTRIBUTION STATEMENT (of the abetrect entered In Block 20, If differe it fron Report)

18, SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reveres aide If necessary end Identify by block number)

Anisotropy

Electromagnetic wave reflectionsMathematical models

4 Sea ice

120. ABSTRACT (Cartrnue a meverse &fI if mcwy atid Ideniify by block ntbor)The contribution of brine layers to observed reflective anisotropy of sea ice at 100 MHz is quantitatively assessed. Thesea ice is considered to be a stratified, inhomogeneous, anisotropic dielectric consisting of pure ice containing orderedarrays of conducting inclusions (brine layers). Below the transition zone, the ice is assumed to have constant azimuthalc-axis orientation within the horizontal plane, so that the orientation of brine layers is uniform. The brine layers arealso assumed to become increasingly well-defined with depth, since adjacent brine inclusions tend to fuse together withincreasing temperature. A theoretical explanation for observed reflective anisotropy is proposed in terms of anisotropicelectric flux penetration into the brine layers. Penetration anisotropy and brine layer geometry are linked to anisotropyin the complex dielectric constant of sea ice. In order to illustrate the above effects we present a numerical method of

D O 14n3 EDITlON OF I NOV 65 IS OBSOLETEUnclassified

SECURITY CLASSIFICATION OF THIS PAGE (When Det Entered)

* ! ,, 1* 4-' tL

UnclngtifiedSECURITY CLASSIFICATION OF THIS PAGE(Wahn Date Rnteisd)

20. Abstract (cont'd)

approximating the reflected power of a plane wave pulse incident on a slab of sea ice. Mixture dielectric constants

are calculated for two polarizations of the incident wave: 1) the electric field parallel to the c-axis direction, and2) the electric field perpendicular to the c-axis direction. These dielectric constants are then used to calculate powerreflection coefficients for the two polarizations. Significant bottom reflection (R - 0.08) occurs when the polariza-tion is parallel to the c-axis. However, when the polarization is perpendicular to the c-axis, the return may be almostcompletely extinguished (R < 0.001). This extinction is due primarily to absorptive loss associated with the conduct-ing inclusions and secondarily to an impedance match at the ice/water interface that results in transmission of thewave to the water without reflection.

ii Unclassified

SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered)

PREFACE

This report was prepared by Kenneth M. Golden, Mathematics Aid, and Stephen F. Ackley, Re-search Physicist, of the Snow and Ice Branch, Research Division, U.S. Army Cold Regions Researchand Engineering Laboratory. Funding for this research was provided by the National Science Founda-tion, Division of Polar Programs, under Grant DPP77-24528.

The authors would like to thank Dr. Wilford Weeks for supplying salinity and temperature dataand for technically reviewing the manuscript, Dr. Anthony Gow for supplying data and general in-formation on sea ice structure, and Dr. Steven Arcone for technical review of the manuscript andconsultation on electromagnetic wave propagation.

4

9.

r~i iii

Jr 7

CONTENTS

PageA b stract ................................................................................................................................... iPreface ..................................................................................................................................... iiiList of symbols ......................................................................................................................... vIntroduction ............................................................................................................................. 1

Anisotropy and sea ice macrostructure ................................................................................ 1Anisotropy and sea ice m icrostructure ............................................................................... 1

A theory of anisotropic radar return from sea ice ..................................................................... 3

Anisotropic electric flux penetration into brine layers ........................................................ 3Implications of normal exclusion, tangential penetration, and brine layer geometry for

dielectric behavior of sea ice ........................................................................................... 5Modeling of electromagnetic reflection from a stratified, anisotropic, inhomogeneous

lossy medium .................................................................................................................. 6Calculation of mixture complex dielectric constants .......................................................... 6Calculation of interfacial power reflection coefficients ........................................................ 7

Calculation of bulk power reflection coefficients ................................................................ 9Calculation of attenuated power reflection coefficients ...................................................... 10Beam spread ........................................................................................................................ 10

R esu lts ..................................................................................................................................... 10

Anisotropic bottom reflections ........................................................................................... 10Anisotropic complex dielectric constants .......................................................................... 11Sensitivity of parameters .................................................................................................... 13Internal reflection: the bumps ........................................................................................... 14

Discussion ................................................................................................................................ 14

Conclusions ............................................................................................................................. 15Literature cited ........................................................................................................................ 15

ILLUSTRATIONS

Figure

1. Rotation of antenna to achieve reflective maxima and minima ...................................... 12. Dendritic plates at ice/water interface ........................................................................... 2

3. Brine layers near the bottom of sea ice .......................................................................... 2

4. Salinity, temperature and calculated brine volume data for Cape Krusenstern ............... 75. Salinity, temperature and calculated brine volume data for Barrow ................................ 8

6. Salinity, temperature and calculated brine volume data for Harrison Bay ....................... 8

7. Schematic diagram for bulk power reflection coefficient calculation ............................. 98. Power reflection profile for Cape Krusenstern, Barrow and Harrison Bay ....................... 109. Real and imaginary parts of the complex mixture dielectric constants at Harrison Bay.. 124 10. One-way power transmission coefficients for normal and tangential polarization at

Harrison Bay .......................................................................................................... 12.4 11. Power reflection coefficient profiles at Harrison Bay ...................................................... 13

TABLES

Table

1. Bottom reflection anisotropies ....................................................................................... 11

iv...

LIST OF SYMBOLS

a, b, c principal axes of an ellipsoid in x,yz-space n index denoting sea ice/sea water interface

du differential element of a surface area (n= +)

norm of a vectorA r outward unit normal vector

B magnetic induction field nk depolarization factor of ellipsoids along axis k

ICI modulus of a complex number C nk(i) depolarization factor of ellipsoids in layer i forpolarization k

d thickness of sea ice layersp dipole moment

D directivity of transmitting/receiving antenna field

D electric displacement field

directivity of receiving antenna Pr power in the load of a receiving antenna

DP directivity of transmitting antenna power radiated by a transmitting antennadq differential element of charge

/--- n compon nt of electric field in ice normal to

brine/ice interface r travel distance between transmitting and re-ceiving antennas

E2n component of electric field in brine normal ceiin ennas

to brine/ice interface r position vector

lt component of electric field in ice tangen- rk(i) interfacial amplitude reflection coefficient for

tial to brine/ice interface interface i and polarization k

E2t component of electric field in brine nor- Rk (i) power reflection coefficient for interface i

mal to brine/ice interface and polarization k

E" applied electric field RA (j) attenuated power reflection coefficient forE tt Poynting vector interface i and polarization k

5i salinity of layer iE0, L 2k0

vectors constant in space and time S surface of an ellipsoidF20, //0 S(i) beam spread factor for interface

Elk electric field inside an ellipsoid due to ini- At plane wave pulse width in timetially uniform field applied along axis k T thickness of sea ice

applied electric field for normal polarization dv differential element of volume

[ applied electric field for tangential polar- 1, velocity of 100 MHz radiation in pure icelation V volume of an ellipsoid

conductivity ol pure ice It' power flowing into ellipsoid per unit volume

conductivity of brine 1n absorbed power density for normal polarizationgk 1i) conductivity of lay5 er i for polariial ion k j1 absorbed power density for tangential polar-

7 distance fr(. n antenna to interlace i ization

4 /4 magnetic intensit, field Z depth in sea ice

/ ctrrent density field Zk 1 bulk impedance of layer i for polarization k

.:efficient of anisotropy for net bottom cyk (U) attenuation constant of layer i for polarization kreflection yk(i) propagation constant of layer i for polarization k

N coefficient of arirsotrop\ for inter facial ,S phase difference between electric fields in icehrottln reflection and brine

number of laveri permittivity of free space

v

e1 complex dielectric constant of host (ice) 0 temperature of layer iC, real part of e1 (dielectric constant) f(O,p) normalized power patterne imaginary part of e1 (dielectric loss) X wavelength of radiation

C2 complex dielectic constant of ellipsoids (brine) X0 free space wavelength

IE2 real part of 2 PO permeability of free spacee2 imaginary part of e 2 v relative volume of inclusionsek() mixture complex dielectric constant of layer tb relative volume of brine in ice

i for polarization along k axes of ellipsoids Vb(i) relative brine ,olume of layer ic4 (i) real part of ek () phase difference between magnetic intensitye"'(i) imaginary part of Ek() field in brine and electric field in iceen real part of mixture complex dielectric con- of free surface charge density

? stant for normal polarization ap bound polarization surface charge density

n imaginary part of mixture dielectric constant temporal period of radiationfor normal polarization

t real part of mixture complex dielectric con- tcond relaxation time for ionic conductionstant for tangential polarization "water relaxation time for water dipole rotations

e imaginary part of mixture dielectric constant 0 azimuthal angle of spherical coordinates

for tangential polarization cW angular frequency of radiation

0 polar angle of spherical coordinates dQ2 differential element of solid angle (= sinOdOdo)

viI

TC

MODELING OF ANISOTROPIC ELECTROMAGNETICREFLECTION FROM SEA ICE

Kenneth M. Golden and Stephen F. Ackley

INTRODUCTIONAxis of

Rotation

It has been established that there exists anisotropyin the strength of the return from impulse radar sound- Antenna o

ings in sea ice (Campbell and Orange 1974, Kovacsand Morey 1978). In this report we quantitatively Maxassess the role of sea ice microstructure in determiningthe nature of this anisotropy. Sea Ie

Anisotropy and sea ice macrostructure Sea WaterThe amplitude of a radar signal reflected from the

ice/water interface may depend markedly on the azi- Figure 1. Rotation of antenna to achieve reflective max-muthal orientation of the linearly polarizing antenna of ima and minima.a radar system with center frequency at 100 MHz(Campbell and Orange 1974). When the antenna is Anisotropy of reflection from sea ice has beenpositioned in the horizontal plane parallel to the sea observed in both first- and multiyear ice with a rangeice surface and rotated about a vertical axis, successive in thickness from 25 cm to over 2 m. Freshwater icemaxima and minima of bottom signal strength are has never been observed to exhibit anisotropy (Camp-spaced at approximately 900 intervals (Fig. 1 ). In the bell and Orange 1974). Anisotropy is observed moremost extreme cases of this anisotropy, the signal ap- often in first-year ice than in multiyear ice and is morepears to be completely extinguished. This means, of pronounced in the younger ice. Where first-year ice iscourse, that the signal returned is of such small ampli- smooth and undeformed, the azimuthal orientations oftude that it cannot be distinguished from background the antenna that correspond to maximum and minimumnoise; i.e. the sensitivity of the receiving instrument bottom reflections stay constant over distances of manyhas been surpassed. kilometers. In areas of broken-up or multiyear pack ice

In addition to anisotropy of bottom reflection, consisting of rotated and refrozen floes, the antennaKovacs and Morey (1978) have observed variation in orientations vary drastically over distances of severalsurface reflection, depending on azimuthal orientation meters.4 of the antenna, when measurements were done at acenter frequency of 625 MHz. The anisotropy associ- Anisotropy and sea ice microstructureated with the ice/air interface at this frequency is, how- Associated with differences in sea ice macrostructureever, much smaller than that associated with the ice/ are differences in microstructure. For example, first-water interface at 100 MHz. There does not seem to year ice generally has a higher brine content than multi-be a well-defined relationship between the directions year ice, because the ice rejects brine with age. We will

F' of minimum or maximum bottom and surface reflec- now review sea ice microstructure and its relation totion. In some cases the directions coincide, in others the reflective anisotropy.the difference approaches 900. Sea ice is an inhomogeneous anisotropic material

r

consisting primarily of pure ice surrounding pocketsof brine. Tiny spherical crystals of pure ice constitute

the first component of newly forming sea ice. Thesespherical crystals grow rapidly into disks and then intodendritic plates. The plane of a dendritic plate coin-cides with the basal plane of the ice crystal that com- C-axis

prises it and is perpendicular to the optic or c-axis of Plates

the crystal. In calm water, the plates freeze togetherto form a smooth skim of ice, with c-axis orientationprimarily vertical. In turbulent water, the plates are

tossed about and broken up so that when they congealinto an ice surface, the c-axis orientation is quite ran-dom. As growth continues downward, the c-axes,through a process of geometric selection, become pre- Figure 2. Dendritic plates at icelwater inter-dominantly horizontal. The layer within the ice where face, elongated parallel to their basal planes,the c-axis orientation changes from vertical or random extending into the sea water below. Seato predominantly horizontal is called the transition water trapped between the plates becomeszone. This zone is about 10 to 15 cm thick and occurs the brine layers (from Weeks and Gow 1979).at a depth anywhere from approximately 2 to 60 cm,

depending on growth conditions ('Weeks and Assur1967, Hobbs 1974, Anderson and Weeks 1958, Weeksand Gow 1979).

The ice/water interface where crystal growth takesplace is not smooth. When ice forms from sea water,ions (salts) are rejected, since salts are extremely in- d.soluble in ice (Hobbs 1974). The rejection of saltscauses an increased solute concentration adjacent to

the slowly advancing solid/liquid interface. This in-creased concentration of salt and an appropriate tem-perature profile produce a zone of constitutionally

supercooled liquid below the interface (Weeks and C

Gow 1979). Tiller (1974) has indicated that the typeof solid/liquid interface associated with constitution- ally supercooled liquid is dendritic or cellular, rather

than planar. Thus, the dendritic plates perpendicularto the c-axes are elongated parallel to their basalplanes and extend into the sea water below (Fig. 2).As further growth occurs, the concentrated sea water b

between the dendritic plates becomes trapped and

makes up the so-called brine layers of sea ice. Sincethe c-axis is perpendicular to the longer dimensionsof the dendritic plates, it must also be perpendicularto the longer dimensions of the brine layers.

Immediately above the ice/water interface, the ice Figure 3. Brine layers (top view) nearis relatively warm and contains a high concentration the bottom of sea ice (a) begin to "neckof brine layers (Fig. 3a). The spacing between adja- with decreasing temperature farther up

cent layers is the thickness of a dendritic plate. Far- in the ice sheet (b) and freeze out intother up the temperature decreases and, consequently, cylinders (c) and elliptical cylindersthe brine layers begin to "neck" (Fig. 3b) and change (d) (from Anderson and Weeks 1958).into rows of closely spaced cylinders (Fig. 3c), and

finally into elliptical cylinders (Fig. 3d). Below thetransition zone, the layers or rows stand up verticallywith the shortest dimension horizontal. Above the

transition zone, the arrangement is more random

2

. ,'

depending on growth conditions. This model of brine A THEORY OF ANISOTROPIC RADARstructure is, of course, idealized. Brine drainage influ- RETURN FROM SEA ICEenced by gravity and temperature gradient is but onefactor that could alter the idealized model. We propose that the asymmetrical geometry of the

Below the transition zone the c-axes lie predom- brine layers causes an anisotropy in the penetration ofinantly in the horizontal plane. Accordingly, layers the impinging electric field into the brine inclusions.of brine in each crystal grain are positioned with their This anisotropic penetration is associated with an anis-two longer dimensions lying in a vertical plane perpen- otropy in the effective complex dielectric constant ofdicular to the c-axis, and with their short dimension the sea ice, which determines the power returned to theoriented horizontally and parallel to the c-axis. Re- receiver.

cent studies of arctic fast ice (Cherepanov 1971,Weeks and Gow 1979, Kovacs and Morey 1978) have Anisotropic electric flux penetrationshown that the c-axes not only have a preferred hori- into brine layerszontal orientation, but also have a preferred azimuthal To illustrate the proposed anisotropic behavior ofdirection within the horizontal plane. Cherepanov the field, we take the following values as the dimen-(1971) found the azimuthal c-axis alignment to be sions of a representative bottom sea ice brine layer.constant for hundreds of kilometers in the Kara Sea. Anderson and Weeks (1958) give the horizontal thick-Weeks and Gow (1979) and Kovacs and Morey (1978) nessb of a typical brine layer as 0.1 mm. Kovacs andfound good positive correlation between the preferred Morey (1978) give the vertical length c of a brine layer

direction of c-axis azimuth and "long term" current as 5b. The horizontal length a of a brine layer perpen-direction beneath the growing ice. Weeks and Gow dicular to the c-axis, determined by examination of(1979) proposed an explanation for the preferred rubbings from sea ice bottom cores (Weeks and Assurorientation in terms of these currents. 1967), is typically 3 mm. An idealized model of a

Preferred azimuthal orientation of c-axes corres- brine layer is a non-degenerate ellipsoid (a > c > b) withponds to preferred azimuthal orientation of brine lay- a surface defined byers. Therefore, in the bottom portions of undeformedice, we expect ordered arrays of brine layers with uni- x2 2 2= (1)

form alignment over a large area. This ordered arrange- a2 b2 c2

ment of c-axes and brine layers is apparently relatedto the reflective anisotropy. Campbell and Orange where a = 3 mm, b = 0.1 mm, and c = 0.5 mm. The(1974) and Kovacs and Morey (1978) have found x-axis is horizontal and perpendicular to the crystalthat a maximum reflection from the ice/water inter- optic axis, the y-axis is horizontal and parallel to theface occurs when the electromagnetic wave is polar- optic axis, and the z-axis is vertical. This analyticalized so that the direction of the electric field parallels form allows approximation of electric flux penetrationthe preferred c-axis direction, or equivalently, when it into a brine layer.

is polarized so that the electric field is normal to the Tinga et al. (1973) derive an expression for the elec-principal brine/ice interface (normal polarization). tric field E21 inside a member of a set of ellipsoidal in-

The minimum reflection from the ice/water interface clusions (brine) of complex dielectric constant E2 , rela-occurs when the pulse is polarized so that the direction tive volume v, and uniform axial alignment, dispersedof the electric field is perpendicular to the preferred in a homogeneous medium (ice) of complex dielectricc-axis direction, or, equivalently, the electric field is constant el, subjected to an initially uniform electrictangential to the principal brine/ice interface (tan- field E directed along one of the principal axesk = a,gential polarization). These findings suggest at least b, c:

two sources for the observed reflective anisotropy:1) uniform crystal arrangement and 2) uniform brine El - C1 (2)

layer arrangement. Hargreaves (1977) has found that C I + nk(1 -V)(e 2 -c )anisotropy of reflection due to oriented crystals ismuch smaller than that found in sea ice. Thus, we wherereject uniform crystal arrangement as the primarycause of the reflective anisotropy and will offer a abe ds (3)theoretical explanation for the observed reflective 2 0 (k2 s(c2

anisotropy of sea ice in terms of the ordered arrays of

brine layers.

t3

is called the depolarization factor (Stratton 1941) of normal component of a harmonically time-dependentthe ellipsoid along the axis k, and depends only on the electric field at the interface between two media,axial ratios. Note that the field inside the ellipsoid isuniform. The applicability of this equation to the cal- -2n =| ' n = -- /1n (6)culation of electric fields inside a brine layer (of larg- Ce2 - 2

est dimension a) at 100 MHz depends primarily on thecondition that a <-< X, which is satisfied for the wave- Everywhere on the brine/ice interface the normal corn-length X z 1.7 m in pure ice. In addition, since brine ponent of the field in the brine must be very smallvolumes (relative volume of brine to ice) near the bot- compared to that in ice, tE 2n I = (3.16x 10-)IE1 n (tom of sea ice reach 0.4 and the electric field inside a During normal polarization, the surface of the brine

brine layer is influenced by the dipole fields of its layer is primarily normal to the applied field so thatneighbors, the derivation of the equation should in- the uniform field inside the brine layer must be of aclude interaction effects. In the self-consistent multi- very small magnitude. Physically, this exclusion arisesphase dielectric mixture theory developed by Tinga from a large depolarizing field within the brine layer

et al. ( 1973), an extra boundary has been introduced created by the buildup of free (ionic) charges and boundbetween the inclusions to account for these effects to polarization charges (from water dipole rotations) on thefirst order. principal interface so that the net field inside the brine

We assume the electric fields are ol th rm E(t) layer is very small. The existence of these effects is

- 0 e-" t and E = 2k0 1no spa- supported by the fact that the relaxation times in brine

tial dependence, wherej = V', o = 27rx 108 rad/s for ionic conduction rCond = 2/wf" 2 -1.3x 10ftt sand (S is the phase difference between fields. We (Stratton 1941 ) and water dipole rotations Twate r f

evaluate eq 2 for the two cases of interest, k = a and 2x 1 1 s (Vant 1976) are both significantly shorter than

k = b, where n a = 9.67 x 10 -3 and nb = 8.39x 10 - are T/2 = 5x 10-9 s, where r is the temporal period of a 100-

calculated by numerical integration. We take c, = c'1 MHz wave.+/c'1' - 3.17+i0.013 (johari and Charette 1975) and

c, = c2 +c2 = 80+/1000 (Vant 1976), and set t' i Case 2. Tangentialpolarizution,= 0.29, where 0 b = 0.29 is the brine volume at 5 cm applied field E = L t Iafrom the bottom of a piece of arctic sea ice, as ob- Taking the real part of t. 2 to be the physical scalar

tained from a polynomial fit of brine volume data. field, we obtain for tangential polarization from eq 2,

Case 1. Normal polarization, Re(L 2,) = (1.90x 10') Re(E,)applied field E - F,, b

Taking the real part of L1b = IIL 11 "" to be (3.54x 10'1) lm(E) (7)the physical scalar field (Jackson 1975), we obtainfrom eq 2 with 6 = tan -' (3.54x 10 -'/ 1.90x 10) = 61.80. The

moduli of the complex fields, or equivalently the am-Re(t2b) = (4.49x 10-) Re(E n ) plitudes of the physical fields, satisfy

-(5.20x 10- ) lm(1_-n) (4) I (.2a 90 - x 10 ILl1

where the mixing of the real and imaginary parts of E

indicates a phase shift, with 6 = tan - ' (5.20x 10- - / = (4.01 x 10')j E,1 . (8)4.49x 104) = 85.10. The moduli of the complexscalar fields, or equivalently the amplitudes of the Therefore, there is a significant penr,ration of nearly

physical fields, satisfy half the applied field into the inclusion for tangentialpolarization. Mathematically, the penetration arises

lb= I 4.49V 10-) I from the boundary condition that the tangential com-"\cos6 / ponient of the electric field must be continuous across

the brine/ice interface,= (5.26x 10-') IEn I. (5)i'L-1 t -2t" (9)

rherefore, the electric field is excluded from the brine

layer for normal polarization. Mathematicall,, this During tangential polarization, the surface of the brine

exclusion arises from the boundary condition on the layer is primarily tangential to the applied field, so thatr

4

I'1

a significant amount of flux penetrates. Physically, averaged over an integral number of periods, then thepenetration, or more accurately the absence of a large first two terms on the right side vanish since sine anddepolarizing field, occurs because the field is directed cosine are orthogonal, and we arc left withalong the interface over most of the surface causingadjacent polarization charges to cancel and free charges W= 1 2 (to travel (though certainly not far) rather than accumu- 92 E20 (12)

late. The field cannot penetrate completely, however,since there is a small depolarizing field created by the where we have replaced the time-averaged surface inte-buildup of charges at the ends of the brine layer. gral with W, the power flowing into the volume V,

measured in W/m 3 . For tangential polarization, E20Implications of normal exclusion, tangential = 4.01 x 10' E0 ; for normal polarization E20 = 5.26xpenetration, and brine layer geometry for 10-3 E0 . Therefore, the ratio of the power losses isdielectric behavior of sea ice

At b_ g2 (4.01x 10-,)2 E2 V+'/zg E2(V/lb) ,2200A bsorp tion - / g(52x1 0- ) 2 0 / l£0 2200Ub

Let S be the surface of an (ellipsoidal) brine layer Wn Y29 2(5.26x 10-3)2 E2 V+ g E'(Vvb)V and E, H,? 2, !1, D2, B2, and/2 be the physical (13)fields on S and in the brine layer. Then we assumethat ? = to cos(oat), E 2 = 7-20 cos(oat+ 6) and H2 = where we assume thatg1 is the conductivity of pureL //, cos(Lit + t) with appropriate dependences for

._2, w ice and that the amplitude of the field in the ice isD2, '2, and 82, where, in general, 6 - . Maxwell's equal to E0 .equations may be manipulated (Lorrain and Corson In other words, we expect a very large difference in1970) to yield a statement of energy conservation (or power absorbed by bottom sea ice for the two polar-continuity of energy flow), izations. The variation is caused by anisotropy of elec-

tric flux penetration into the brine layers, which in turn- I x H -

+ -D2 6 + "-2 d is related to anisotropy in the am ount of brine layerd t ( 2. surface situated normal to the electric field.

S Because the tangentially polarized wave "sees" (pen-

+ f/2 E 2 dv (10) etrates) the brine layers but the normally polarizedv wave does not, significant conduction currents are set

up throughout the brine layer during tangential polar-where n is an outward unit normal vector. The rate at ization but not during normal polarization. Note thatwhich energy (represented by the Poynting vector) we are primarily considering conduction effects,

flows into the brine layer is equal to the increase in since 100 MHz is below the resonant frequency forelectromagnetic field energy stored in the brine layer water dipole rotations. Thus, for normal polarization,per unit time plus the energy removed by conversion there is a small imaginary mixture dielectric constantto heat (conduction losses) per unit time. If one as- (en - Wn) with a significant signal transmitted throughsumes that the brine is linear, isotropic, ohmic and the medium and subsequently returned to the receiver.non-magnetic, and that the fields are uniform inside For tangential polarization there is a large imaginarythe brine, then eq 10 becomes mixture dielectric constant (E',' Wt ) with higher atten-

uation and much less signal returned.H'nIda = -(20 /0 2 +g2E

"S 2dt PolarizabilityIn addition to anisotropic absorption of the wave,

= -oVle'2 eOE20 cos(Wot+6) sin(oat+6) the asymmetry of the brine inclusions causes aniso-tropy in the polarizability of the sea ice, and conse-

2+0 H20 cos(ot+t) sin(cwt+t) quently in the real part of the effective dielectric con-

2-S stant. The dipole moment, defined (Reitz and Milford

+92 E20 cs 2 (t+6)] (11) 1967) by

where/a 0 = 41rx 10-7 N/A 2 is the permeability of free p = f I dq (14)

space, 0 = 8.854x 10-12 C2 /N m2 is the permittivity

of free space, and g 2 is the conductivity of brine in for a brine layer with surface S takes the formmho/m. If this equation is divided by V and time-

5

S=J7(oi + Op)da (15) where i 1,2 ...= 1 n, since, for example, what the re-ceiver measures as the bottom reflection is influencedby the top reflection. These bulk power reflection co-

where a, is the free (ionic) surface charge density, O efficients are then used to calculate attenuated poweris the bound (water dipole rotation) polarization sur- reflection coefficients Rk (i), where i = 1, 2,...,n. Thisface charge density, r is a position vector, and du is a calculation takes losses (attenuation) into account, asdifferential element of charge. During tangential polar- determined by the Ek (i). Finally, the power reflection

ization, u, and o contribute to the integral in eq 14 coefficients Rk (i) are calculated from the Ru' (i) byprimarily when I is very large, so that the dipole mo- including the effect of beam spreading. The reflectivement p of the brine layer is large. During normal po- behavior of the radar pulse of small width in frequencylarization, when the applied field parallels the short space is approximated by analysis of the center frequencyaxis, .Op and o, are distributed more evenly, so that the (100-MHz) component of a plane wave pulse.dipole moment of the brine layer is smaller. ISeevan de Hulst (1957) lor calculations of these dipole Calculation of mixture complexmoments for the two polarizations. I The dipole mo- dielectric constantsments p of the medium determine its polarization P, Tinga et al. (1973) derive an expression for the con-which is related to the real dielectric constant by P plex dielectric constant ek of a mixture consisting ofeO(c'- 1) . Therefore, for tangential polarization ellipsoids (brine) of complex dielectric constant e ,

there is a larger real dielectric constant than for normal relative volume v, and uniform axial alignment, dispersedpolarization, in a homogeneous medium (ice) of complex dielectric

We hope that the preceding discussion provides a constant c1 when the mixture is subjected to an initi-physical basis for understanding the observed reflective ally uniform electric field directed along one ol theanisotropy. We feel that the complex interplay among principal axesk = u, b, c of the ellipsoids:the effects described and their relative contributionsto the reflective anisotropy is best examined with a Ck C I + n ( 2E C) c (16)numerical model of sea ice reflections, which we will Inow present.

where nk is the depolarization tactor of the ellipsoidalong axis k. Since we consider the sea ice to be strati-

MODELING OF ELECTROMAGNETIC fied, eq 16 takes the for mREFLECTION FROM A STRATIFIED,ANISOTROPIC, INHOMOGENEOUSo E(,)= 1 + In (I) (cr- - )LOSSY MEDIUM I n -(jl41 -uh i)t I (c -c,)c

We wish to obtain reflection profiles of sea ice of = 4(i) +/4(i) I TIthickness T, i.e. graphs of power reflection coefficients(power received from a given depth/power transmitted) where the brine volume Ob(i) and depolarization tactor

vs depth, for the two polarizations of interest. The sea nk(i) of the ellipsoids are varied tor each lavei t toice is assumed to be composed of layers of uniform account for the change in physical properties ol the ice

thickness d, which we shall take as 10 cm, where the with depth, and k denotes polarization, either tangen-number of layers is V = T/d. ("Layer" her, denotes a tial t or normal n. Equation 17 is evaluated using ap-particular depth interval, e.g. 150 to 160 cm.) To ob- propriate frequency-dependent values for cI and ( .

tain a reflection profile, we calculate complex dielec- We assume that the dielectric constants of the ice andtric constants ck(i) for each layer i, where i = 1,2,....V, brine, cl and c,, are constant with depth. See Vantand for each polarization, normal and tangential. (1976) for a discussion of the applicability of eq 17These dielectric constants (which are actually the first to time-varying fields.two components of the diagonal dielectric tensor) are The brine volume vb(i) is varied according to poly-used in a calculation of interfacial power reflection co- nomial fits of data calculated from salinity and tempera-

"4 efficients Rlk(i), where i 1, 2,...,n and n = V+ I . Rl(1) ture profiles obtained from arctic fast ice by W.I . Weeks

denotes reflection from the air/ice interface and R1 (n) and A.). Gow.* Data are considered from Cape Krusen-denotes reflection from the ice/water interface. The stern, Barrow (Chukchi Sea) and Harrison Bay. Theinterfacial power reflection coefficients are used in acalculation of bulk power reflection coefficients Rl (i) *W.l . Weeks and A.I. Gow, CRRL L, personal communication, 1979.

6

Ao

Brine Volume0 0050 0100 0 150 0200

vJ(Z) 111119500 9)Z'-(7.70xIO UlZ -4

Salinity (%o) TompeoturarC) 20- (1.7000"M - 4.24001 -

02 4 6 8 10 12 -10 -8 - -4 -2

20 240E. 40

CL 60-060-

00L 80

a. Sulinitj, umb. tepeatre Chiafied brinie '0/june dAaa wil; po/lnnonia/ fii (/I,-1101 e, dlepth.

Injure 4. Saint, tempera!ture und calculat'cI brine itv/nine data for Cape Krusens tern.

Salinity and temperature pro-iles for thle three sites are thc brine layers (Fig. 3) with a limit of randomly dis-shown in Figures 4a, 5a and 6a, and the brine volumne persed tubules (a b ) at the top. The vertical (c) dimen-profiles are shown in Figures 4b, 5b and 6b. For a sion is decrealsed to a value less than a = b at thle top togiven I 0-enl layer i, thle brine vo)'lme 10h (') is Calculated indicalte that the longest dimensions of the ranlomlyusing the equation of I rankenstein and Garner (given disper sed tubules have a tendency to be hor i/ontal.in Weeks and Assur 1967), Therefore, at thle top of thle ice there are fat, round

disks whose shortest dimension is vertical, and at thle

U00i) Sj_ 1>9.185 1 0.532 (18) bottom there are f-lat, elongated disks whose shortest101 b d imension is hii,on tal. At present, very l itt le inf or -

mlat ion is available concerning the detailed geomneti ofwhere -Si is the salinity of laver i expressed in parts per- br ine Structure. The model we use is a rough first orderthousand, 0i is the temiperature of laver i expressed in (linear ) approx~imnation designed only to reflect thle grossdegrees Celsius, and 1)b(/) is expressed as a dimension- leatures of brine structure: anisotriopy near the bottomless rat in. Polysno m ial fit s were takeni to silloo t h the anid isotropy near the top.discontinuities imposed by the sampling procedure, aLsWell aIs to allow for variation oif the laver thickness dl. Calculation of interfacial power

Recall that a depolari/ation lactor I r a particular reflection coefficients4 ax is depends only onl the alxial ratios of thle ellipsoid. We will now calculate interfac ial power reflect ionThlus, we var y thle Ilk (i) with depth by changing thle coeff icients R' (i) (power reflected by interlace i/'powetrelationships between the a xes. In the bot tom 10 cm, incident onl interl ace i) at each interface i for thle twowe take the relationships to be determined by a~hb(- polariiations. The character istic hulk imipedlance Zk W)30:1:5, so as to model the well-defined brine layers. of layer i for polar i/ation along axis k is dlef ned (Ward

Throughout the ice sheet we keep 1b constant butl var y 1967) byU a and ilinear ly so that u:b:(i I 1: 1:0.5 at the top oif

the ice sheet. Fihe linear change in the r atio a//) is to /() 19simulate the necking and subsequent free/ing-out of ()

7

Salinity (/,) Temperature (C)Salinity (%o) Temperature(*C) 2 4 6 8 10 12 -20 ,16 -12* -8 -4

4 6 8 1012-20 -16 -12 -8 -4 o 00

20-20-

40-40

60-60""

- - '80-800

o o

100

100-

120120

140140-

160160 - 1 , I I

a. Salinity and temperature. a. Salinity and temperature.Brine Volume

Brine Volume 0 0.10 020 030 0400.050 0.100 0.150 0200 ,1T--r -- I ! , I r-

4 * V(Z) 13.30x110Y)ZI-i6.I4x0-h)z-. 1Z) z 11.17xlO',)Z,(1.112xlO-4)Z 2 '20Z =1.-lOl~ll!l~Z

20 + 17.23x104)Z + 1.74x10-2 + (2.7uIZ+ 1.UxlO-'

40- 4040'

60-60-

-I ,J80

- O.4

100 -

12020

140-

~~140 -4

te e wh 160-

160 L , I I J . _ _ _ 1 _

b. Calculated brine volume data with polynomial fit. b. Calculated brine volume data with polynomial fit.Figure 5. Salinity, temperature and calculated brine vol- Figure 6. Salinity, temperature and calculated brine vol-ume data for Barrow (Chukchi Sea). ume data for Harrison Bay.

I8

where Yk() is the propagation constant of layer i de- Calculation of bulk powerfined by reflection coefficients

Consider a homogeneous slab of pure ice (assumed

/k () = opow2e k(i) +ip 0o~gk(i) , (20) lossless) of thickness d lying below a homogeneous

half-space of air and above a homogeneous half-space

gk(i) is the conductivity of layer i for polarization of sea water. Let a plane wave pulse of duration At

along the k axis of the ellipsoids, and w = 2nrx 108 traveling through air be normally incident on interface

rad/s. Since we assume that the losses in sea ice at 1. Further assume that At << d/v 1, where v, is the wave

100 MHz are primarily due to conduction effects, i.e. velocity in ice. The primary pulse returned to the air

gk(i) = e0 we e(i), eq 20 becomes from interface 2 has the following bulk power reflec-

tion coefficient (power returned to air by the inter-

coV'6 0p0 ek . (21) face/power incident on ice slab, without attenuation):

The complex amplitude reflection coefficient rk(i) at R8(2) = [1 -R'(1 ) • RI(2) (1 -RI(1 ) .an interface i depends upon the mismatch of the bulk

impedance Zk(i- 1) of layer i-I above the interface A secondary pulse reflected back into the air by inter-

and the bulk impedance Zk(i) of layer i below the face 2 has the following bulk power reflection coefficient:

interface:

rk(i) = Z (- 1) - Zk(i) (22) RB( 2 ) = [ -R'(1) R'(2) R (2) [1 -R'(1)I

4(1-1) +Zk(i) There are infinitely many of these reflections. For our

On substitution of eq 19 and 21 this becomes model of a multi-layered slab of sea ice we neglect mul-

tiple reflection effects beyond first order and consider

-A only primary reflections, so that the bulk power reflec-

r /) - - - - ' (23) tion coefficient of interface m for polarization k is

|/k + r(k;i11 given by

Note that this expression depends on frequency only m-t

through the dispersive nature of the dielectric con- RB(m) = 1 [1-R'(i) 12 Rk(m) (25)

stants of the constituents of the system, sea water, ice, i=1

brine, and air. Finally, the interfacial power reflection for m = 2, 3,. n, and

coefficient R' (i) at interface i is obtained from the

complex amplitude coefficient through RB(m) = Rk(m) (26)

Rk(i) rk(i)*rk(i) (24) for m = 1. Figure 7 gives a schematic of the situation.

where * denotes complex conjugation.

Air RA (1)R '() R"(i) R (n)

sea _ R' _)___-" Ice

Snn.n

Water Time

Figure 7. Schematic diagram for bulk power reflection coefficient

calculation.

t 9

t4

Calculation of attenuated power lo obtain the final power reflection coefficients Rk(i),reflection coefficients we multiply each RA (i) by the beam spread factor 5(i),

The attenuated power reflection coefficient R" (i)for interface i (power returned to air by interface i/pow- Rk(i) = S(i) R A (i) (33)er incident on ice slab) is calculated from Rt(i) by in-

cluding losses from travel through the sea ice. The am- ,-'ithplitude of a plane monochromatic wave traveling oneway through a lossy layer i of sea ice of thickness d S(i)= 1 6.83 2

and complex dielectric constant ek(i) is decreased by P, 4. (34)the factor e "-k(0", where ak(i) is defined by von Hippel(1954) as where h is the distance from the antenna to interface i.

Since reflection measurements are often done with !beCk(i) =E/I + i 1 L\ (27) antenna resting on the ice, we normalize the S(i) so

X0 ( 2 k that S() = 1 ; i.e. there is no beam spreading for thesurface reflection.

where X0 is the free space wavelength, and k indicates The above-described numerical method for obtain-polarization. One-way power, therefore, decreases by ing ret lection profiles was carried out on the computera factor [e'k(i)d]2, which may be termed a power at Dartmouth College, Hanover, New Hampshire. Wetransmission coefficient for layer i, and we define the will now present the results of our calculations.attenuated power reflection coefficients RA

(in) bykl(i) 14"4R'(m) (28) RESULTS

Anisotropic bottom reflectionsfor i = 2, 3. n, and Our calculations show anisotropic bottom reflections

from sea ice at 100 MHz. Figure 8 gives the calculatedR"' (m) R l<(m) (29) reflection profiles of the two polarizations for the three

for m =I. 0

Beam spreadWe estimate beam spreading effects with the Friis

transmission formula (Kraus 1953), which gives the 20-1ratio ol the power in the load of a receiving antennaP, to the power radiated by a transmitting antenna Pt

in terms of the distance between the antennas r, thewavelength A, and the directivities of the transmitting 40and receiving antenna, D, and Dr, respectively,

"" P ,_ D D 1) 2 (30)

Pt 4r r

The di'ectivity can be expressed as I

)v = 4(31)f f(,,5)d A2 8o

where f(O,O) is the normalized power pattern. For 1 Isimplicity we assume that the transmitting/receiving 0 0030 0.060 0.090 0.120

simplcitywe asumePower Received/Power Tronemitldantenna in our study radiates energy uniformlh over a

f, cone subtending a total polar angle of 900. The direc- a. Cape Krusenstern (in the bottom layer Vb 0. 17).p' tivity D ~ = D)t then becomes Figure 8. Power reflection profile of Rk(i) for Cape

1) 4 ::t6.83. (32) Kusenstern, Barrow and Harrison Bay. E, denotesrf2" dpf n/

4 sinO dO tangential polarization, E, denotes normal polariza-n 0 tion.

10

0

0 . I _ .

20 20

20

40

40

60

60

E 80

E 80-

o00a7

100--

120 IEt

120-

140

140 -

160- En

1E, I I0 0025 0.050 0.075 0100 0 0025 0.050 0.075 0100

Power Received/Power Transmitted Power Received/Power Transmitted

b. Barrow (in the bottom layer Vb = 0. 12). c. Harrison Bay (in the bottom layer Vb = 0.29).

Figure 8 (cont 'd.

Table 1. Bottom reflection anisotropies. is not the case for K since net reflections are deter-mined by attenuation and reflections above the bottom

Site Ub(/ - d/2) KI

K interface.

Cape Krusenstern 0.17 2.2 41Barrow 0.12 1.9 56 Anisotropic complex dielectric constantsHarrison Bay 0.29 ;O 800 In our numerical model, reflective anisotropy can

only exist with anisotropic dielectric constants. Figure

sites. Table 1 gives the bottom layer brine volume, the 9 shows the dielectric constant profiles at Harrison Baycoefficient of anisotropy for interfacial bottom reflec- for both normal and tangential polarizations. The anis-,ion K' = R1(n)IR'(n), and the coefficient of anisotropy otropy is most pronounced in the lower region of thefor net bottom reflection K z R(n)/Rt(n) for each site. ice where the brine volume and a/b ratio are high, i.e.Note the correlation between bottom layer brine vol- where the brine layers are numerous and well-defined.ume and bottom interfacial anisotropy in Table I. This The wave is highly attenuated in these lower regions¢t11

CD

4c 0

1y000

(w) tLudaa -

00

0

c00

00

00

0

0M 00 N

(ujo) #4daoi

V 12

20 20 -I~

III

40 40

60' 60

80 .2 80

Ch

100 100-

120 - 120

iEt

140 140-

160 E160-

0 0025 0050 0075 0.100 0 0.025 0.050 o.075 0.100

Power Received/Power Transmitted Power Received/Power Transmitted

a. .:h:c = 20:1:5 at bottom. b. a:b:c = 50.1:5 at bottom.

Figure 17. Power reflection coefficient Rk(i) profiles at Harrison Bay.

because of the very large contribution of e" for tan- charges can build up at the ends of the brine layers,gential polarization, as suggested previously. Figure 10 rendering the sea ice highly polarizable, more so thanshows the one-way power transmission coefficients pure brine with no interfaces.I e'e(i)d12 for Harrison Bay associated with this atten- The combination of the large real and imaginaryuation. The ratio of the imaginary dielectric constants parts of the mixture dielectric constant for tangentialfor the bottom layer at this site, e''n = 47.3/0.027 polarization cause the bulk impedance of the bottom1800 is roughly in agreement with the ratio of power sea ice layer to be similar to that of the water below.losses in eq 13, Wt]W n - 2200, the calculation of Consequently, after downward propagation, the remain-which was based on normal exclusion and tangential ing energy of the tangentially polarized wave tends topenetration of electric flux. be transmitted, rather than reflected at the ice/water

We see that the real part of the complex mixture interface, as is shown in Table 1 by the K1. The nor-dielectric constant for tangential polarization at the mally polarized wave encounters an impedance mis-bottom of the ice at Harrison Bay has become quite match and is reflected.high (109), in fact higher than that of brine itself (80).

, The finite extent of the brine layers causes them to Sensitivity of parametersbehave as marroscopic dipoles. Free and polarization If one holds axes b and c constant while decreasing

13

a, the anisotropy decreases. Figure 1 la gives the re- reflection since the higher dielectric constant of theflection profile for bottom a:b:c = 20:1:5. The in- ice for tangential polarization causes the Wave velocitycrease in bottom return for tangential polarization is to decrease. Figure 4 of Campbell and Orange (1974)due to the increase in surface area of the ellipsoids can be interpreted to show retun higher in the ice sheetpresented normally to the field, which results in less when the antenna is oriented for minimum bottom re-electric flux penetration and less attenuation, as has flection. We leave this very interesting aspect of thebeen previously shown. If the a axis is increased, as reflective anisotropy open to more exhaustive experi-in Figure I I b where the bottom axial ratios are a:b:c mentation.= 50:1:5, then the return of the tangentially polarizedwave is decreased primarily because of higher attenua-

tion from increased flux penetration into the brine DISCUSSIONlayers. Note that the bottom return for normal polar-;zation is constant for Figures 8c, II a and I I b since We have assumed extreme order in the microstruc-electric flux is effectively excluded from the brine ture of sea ice. Effective axial ratios for brine inclusionslayers in all cases. at a given depth or region within sea ice are most prob-

If one holds axes u and b constant while increasing ably distributed about some mean, and there is certainlyc, the anisotropy decreases; the bottom return for variation in the orientations of the brine inclusions.tangential polarization increases while that for normal However, the standard deviations for the preferred bot-polarization stays constant. The reasoning for this tom c-axis azimuth given by Weeks and Gow (1979)effect is the same as that above: an increase in c (like are between 50 and 150, indicating a higher degree ofa decrease in a) allows a larger depolarizing field to be ordering. Our purpose was to show that if one viewscreated in the ellipsoid so that less of the wave will be brine inclusions as finite, anisotropic, conductingattenuated. Decreasing the layer thickness d smooths bodies that are small compared to wavelength, thenthe impedance mismatches at interfaces within the sea the observed reflective anisotropy follows naturallyice and thus decreases the magnitudes of the interfacial from the behavior of the electromagnetic field aroundreflection coefficients. and in the bodies, as specified by Maxwell's equations.

To better illustrate mechanisms determining reflectiveInternal reflection: the bumps anisotropy, we have taken a simplified model of sea

It is very interesting to note the appearance of an ice. Examination of these limiting cases may renderinternal reflection located at a depth of about 2 T/3 the observed data more understandable.(Fig. 8a, 8c, and 1 la) for tangential polarization. In For instance, in our theoretical explanation of re-the model this bump arises from a superposition of flective anisotropy we concern ourselves primarily withtwo effects. A large brine volume gradient and an in- a limiting case of brine structure, namely brine lavers

crease in axial ratio with depth first combine to create (Fig. 3a, b). Throughout much of the ice sheet, theimpedance mismatches between layers, with resulting brine structure takes the form of rows of vertical, cigar-interfacial reflections starting up in the ice sheet and shaped inclusions with a top view similar to that inextending downward to the bottom. When the ice Figures 3 c and 3d. However, even if there is no hori-slab is very lossy at the bottom (for example, when zontal anisotropy in the inclusion (u:b:c = 1:1:5),a:b:c = 30:1:5) the bottom reflections are cut out by there will be an anisotropy in electric flux penetration,attenuation, leaving the bump higher in the ice sheet .is long as the distance between adjacent inclusions is(Fig. 8c). [he position ot the hump may be moved less than the distance between adjacent rows of inclu-lower in the ice sheet by varying the axial ratio func- sions. During normal polarization, induced dipolestion with depth so that larger a/b ratios ale not en- interact ;o that in the region between adjacent inclu-countered until the lowest portions of the ice sheet, sions where the electric field is tangential to the surface,e.g. f(z) - + /(z - T), where a and 3 are constants flux is diminished. Consequently, penetration of theused to fit the boundary conditions of isotropy near field into the "cigars" for normal polarization is lessthe top and maximal anisotrops near the bottom, than that for tangential polarization, as long as the

Kovacs and Morrev (1 979) have postulated the above distance relations are kept. However, reflectiveexistence of this bump in explaining how reflective anisotropy associated with these ordered "cigars" willanisotro p, can coexist with travel-time (and apparent be smaller than that associated with the brine la\ ers.dielectric constant) isotrops. Ihey hypothesize that An initial impetus for the present research was ourthe refic, Kion associaleo with the bump of tangential dissatisfaction with the parallel plate waveguide modelpilar izt in (which they term an upward shift of the proposed by Kovacs and Mores (1978) to explain the

electrimagnetic boundarv) appears as a small bottom anisotropy phenomenon. In this model, the brine

I14

structure near the bottom of the ie is assumed to be- can only be obtained by coring a small sample of ice.have as a parallel plate waveguide. The frequency of A methodology that could extend this information to100 MHz is well below cutoff for the waveguide, so line and area measurements such as radar soundingthat attenuation rather than propagation exists for would be valuable in future engineering and scientificpolarization parallel to the plates. The most funda- investigations of sea ice.mental problem with this theory is the lack of evidencefor the existence of well-defined plates of the type re-quired by their arguments. We feel that it is more LITERATURE CITEDnatural to consider the brine structure as consistingof individual, finite, anisotropic bodies rather than Anderson, D.L. and W.F. Weeks (1958) A theoretical analysis

continuous plates. of sea ice strength. Transactions, American GeophysicalUnion, vol. 39, no. 4, p. 632-640.

Campbell, K.t. and A.S. Orange (1974) The electrical aniso-tropy of sea ice in the hori/ontal plane. iournal of Geo-

CONCLUSIONS physical Research, vol. 79, no. 3, p. 5059-5063.Cherepanov, N.V. 11971) Spatial arrangement of sea ice crystal

The reflective anisotropy observed in sea ice can be structure (in Russian). Problemy Arktiki Antarktiki, vol. 38,explained by consideration of the geometrical asym- p. 137-140. (English translation, National Technical Infor-metries inherent in the brine structure of sea ice with mation Service, Springfield, Va.)

Hargreaves, N.D. (1977) The polarization of radio signals ina high azimuthal order of c-axis orientation. Axial the radio echo sounding of ice sheets. /ournai of Physics,ratios of the brine layers of the order of 30:1:5 give D: Applied Physics, vol. 10, p. 1285-1301.a reasonable level of power returned to the ice surface Hobbs, P.V. (1974) Ice physics. Oxford: Clarendon Press.in the direction normal to the brine layers (parallel to Jackson, .D. (1975) Classical electrodynamics. New York:

the c-axis) while significantly attenuating the power John Wiley' and Sons.tohari, G.P. and P.A. Charette (1975) The permittivity and

tangential to the brine layers (perpendicular to the attenuation in polycrystalline and single-crystal ice Ih atc-axis). 35 and 60 MHz. /ournal ol Glaciology, vol. 14, no. 71,

The reflective anisotropy is understood by consid- p. 293-303.ering the amount of electric field that penetrates the Kovacs, A. and R.M. Morey (1978) Radar anisotropy of seabrine layers for the tangential and normal polariza- ice due to preferred azimuthal orientation of the horizontalc-axes of ice crystals. Journal of Geophysical Research,tions. Large electric field penetration in the tangential vol. 83, no. C12, p. 6037-6046.case allows conduction effects to attenuate the wave Kovacs, A. and R.M. Morey (1979) Anisotropic properties ofand reduce the power returned from the ice/water in- sea ice in the 50-150 MHz range. /ournal of Geophsical

terface. Impedance matching at the ice/water inter- Research, vol. 84, no. C9, p. 5749-5759.Kraus, I.P. (1953) Electromagnetics. New York: McGraw-

face in the tangential case also allows more of the in- Hill.cident power to penetrate into the sea water instead Lorrain, P. and D.R. Corson (1970) Electromagnetic fieldsof being reflected by the interface, and waves. San Francisco: W.H. Freeman.

The parameters of interest for the magnitude of Reitz, I.R. and F.I. Milford (1967) Foundations at electro

the reflected power in the model calculations are the magnetic theory. Reading, Massachusetts: Addison-WesleyPublishing Co.

brine volume profile with depth and the axial ratios Stratton, I.A. (1941) Electromagnetic theory. New York:of the brine inclusions relative to the polarization of McGraw-Hill.the wave. Variation in these parameters during model Tiller, W.A. (1964) Dendrites. Science, vol. 146, no. 3646,calculations indicated that reflection profiles would p. 8 71-879.be substantially changed by the imposed variations. Tinga, W.R., W.A.G. Voss and D.F. Blossey (1973) General-

ized approach to multiphase dielectric mixture theor,.Further experimental work relating the observed re- Journal of Applied Physics, vol. 44, no. 9, p. 3897-3902.flected power to the details of the sea ice microstruc- van de Hulst, H.C. (1957) Light scattering by smallparticles.ture (the axial ratio variations and distributions with New York: John Wiley and Sons.

depth, and brine volume information) could be used Vant, M.R. (1976) A combined empirical and theoretical studyto establish one-to-one relationships between power of the dielectric properties of sea ice over the frequencyrange 100 MHz to 40 GHz. Ph.D. thesis, Carleton Univer-levels returned from certain depths and ice microstruc- sity, Ottawa, Ontario (unpublished).ture. If these relationships can be established, radar von Hipple, A.R. (1954) Dilectrics and waves. Cambridge,sounding of sea ice could then be used as a nonde- Massachusetts: MIT Press.

U structive "spectroscopic" tool, giving information on Ward, S.H. (1967) Electromagnetic theor for geophysical

the microstructure variations that ultimately control applications. In Minina ( eophysi %. Tulsa, Oklahoma:Society of Exploration Geophvsicislt.the strength and other important physical properties Weeks, W.V. and A. Assur (1967) lhe mechanical properties

of se. ice. At present, microstructure information of sea ice. CRREL Monograph II-C3. AD 6627 16.Weeks, W.. and A.l. Gow (1979) Crystal alignments in the

fast ice of arctic Alaska. CRREL Report 79-22. ADA077188.

I1

Golden, Kenneth M.Modeling of anisotropic electromagnetic reflection from

sea ice / by Kenneth M. Golden and Stephen F. Ackley. Hanover,Hanover, N.H.: U.S. Cold Regions Research and EngineeringLaboratory; Springfield, Va.: available from National Tech-nical Information Service, 1980.vi, 15 p., illus.; 28 cm. (CRREL Report 80-23.)Prepared for National Science Foundation by Corps of En-

gineers, U.S. Army Cold Regions Research and EngineeringLaboratory under Grant DPP77-24528.Bibliography: p. 15.1. Anisotropy. 2. Electromagnetic wave reflections.

3. Mathematical models. 4. Sea ice. I. United States.Army. Corps of Engineers. II. Army Cold Regions Researchand Engineering Laboratory, Hanover, N.H. Il. Series:CRREL Report 80-23.

U S GOVERNMENT PRINTINGOFFICE 198- 700-418 250

'V

I'I

a